基于指数效用无差异价值过程的不完备市场下的可违约期权的定价模型

本文研究不完备市场情况下的可违约期权的动态指数效用无差异定价。不同于大多数的可违约期权定价文献，本文没有假定鞅的不变性，即通常的H 假设，而是通过信息流的扩张和测度的变换，将信用风险敏感的资产转换为一个G 局部鞅，其后引入一个具体的倒向随机微分方程（BSDE），并证明该方程解的存在性与唯一性；然后利用无差异价值过程C_t（B，α）在最小熵鞅测度下对一般的投资策略为上鞅，而在最优投资策略下为鞅的事实，证明无差异价值过程C_t（B，α）就是BSDE 的解，从而给出可违约期权的定价。

A pricing defaultable claim model based on exponential utility indiference value process in an incomplete market

We study the dynamics of exponential utility indiference value process Ct（B, α） for a defaultable claim in an incomplete market. Other than most of papers dealing with defautable claim, we do not assume the hypothesis of invariance of martingale that is H hypothesis. We frstly transform the default sensitive assets S to be a local martingale through progressively enlargement of fltration and changes of measure. Then, we introduce a specifc backward stochastic diferential equation（BSDE） and prove the existence and uniqueness of the solution. Finally, we prove the exponential utility indiference value process Ct（B, α） is the solution to the BSDE based on the fact that Ct（B, α） is a supermartingale for investment strategies and a martingale for optimal strategy under the minimal entropy martingale measure.